3-2. For events A and B within a sample space S, let P(A) = 0.4, P(B) = 0.3, and P(A ∩ B) = 0.1. Are events A and B mutually exclusive? Are they collectively exhaustive? Are they independent events? Also, find:

(a) P(A)

(b) P(A ∪ B)

(c) P(A|B)

(d) P(B|A)

(e) P(B|A)

(f) P(A ∩ B)

(g) P(B|A ∪ B)

(h) P(B|A ∩ B)

(i) P(A ∩ B|A ∪ B)